Painlevé Property
المؤلف:
Slavyanov, S. Yu. and Lay, W.
المصدر:
"Painlevé Property." §5.1 in Special Functions: A Unified Theory Based on Singularities. Oxford, England: Oxford University Press
الجزء والصفحة:
pp. 232-236
3-7-2018
981
Painlevé Property
Following the work of Fuchs in classifying first-order ordinary differential equations, Painlevé studied second-order ordinary differential equation of the form
where 
is analytic in 
and rational in 
and 
Painlevé found 50 types whose only movable singularities are ordinary poles. This characteristic is known as the Painlevé property. Six of the transcendents define new transcendents known as Painlevé transcendents, and the remaining 44 can be integrated in terms of classical transcendents, quadratures, or the Painlevé transcendents.
REFERENCES:
Slavyanov, S. Yu. and Lay, W. "Painlevé Property." §5.1 in Special Functions: A Unified Theory Based on Singularities. Oxford, England: Oxford University Press, pp. 232-236, 2000.
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